Can I patent a board game?
No. Abstract ideas such as rules for playing a game are not patentable subject matter.
However, you can register your board design. The design registration will last for 10 years. During the term of the design you can mark your product, its packaging and your advertising with the term REGISTERED DESIGN
You'll need a registered design if you want to licence your board design to third parties to manufacture. Otherwise, the board design is a mere idea over which you can't claim a monopoly.
Copyright in the particular expression of your idea can be easily worked around and expires as soon as you've commercially applied the design (i.e. made over 50 copies of the board).
The brand name of the board game, such as MONOPOLY, is also important and should be registered to ensure to obtain a monopoly on that word and stop others from using deceptively terms.